Mise à jour 29 juin 2024

*Description of the image: Warren McCulloch (1898-1969) and Walter Pitts (1923-1969) introduced what they called "formal neurons." These formal neurons are a mathematical abstraction of biological neurons, designed to represent their functioning in a simplified yet sufficiently precise manner to allow for mathematical analysis. *

McCulloch, a neurophysiologist, and Pitts, a logician, conceptualized formal neurons as computational units to construct artificial neural networks in their 1943 paper titled "A Logical Calculus of the Ideas Immanent in Nervous Activity."

In this publication, they presented a simple yet powerful mathematical model of neurons and neural networks. Their objective was to understand how the brain could perform logical operations, similar to those performed by a computer.

A formal neuron is a mathematical and computational representation of a biological neuron. It has multiple inputs and one output, corresponding to the dendrites and the axon hillock of the biological neuron, the starting point of the axon. The excitatory and inhibitory actions of the synapses are represented by numerical coefficients (synaptic weights) associated with the inputs.

Within their model, a formal neuron takes binary inputs (activated or deactivated) from other neurons or external sources. Each input is weighted by a specific weight, which can represent the strength of the synaptic connection between neurons in the biological model.

Based on the weighted sum of its inputs, the formal neuron produces a binary output, which can be activated (1) or deactivated (0). This output is usually determined by applying an activation function, such as the threshold function, which converts the weighted sum of inputs into a binary output according to a predefined threshold.

McCulloch and Pitts used these formal neurons to construct artificial neural networks capable of performing logical operations such as conjunction (AND), disjunction (OR), and negation (NOT). They demonstrated that even with these simple connection rules, it was possible to build neural networks capable of performing complex logical operations.

This formalization of neurons was crucial for enabling mathematical analysis and modeling of neural networks, thus laying the foundation for future research in artificial intelligence and computational neuroscience (the application of computer science to the understanding of the nervous system).

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